Kayles on the Way to the Stars

We present several new results on the impartial two-person game Kayles. The original version is played on a row of pins (“kayles”). We investigate variants of the game played on graphs. We solve a previously stated open problem in proving that determining the value of a game position needs only polynomial time in a star of bounded degree, and therefore finding the winning move – if one exists – can be done in linear time based on the data calculated before.